Optimized cluster theory of polymer blends: General formulation and application to isotopic polyethylene mixtures

A theory for the thermodynamic properties of binary polymer blends was developed and applied to predict the compositional dependence of the effective chi parameter χS in model isotopic polyethylene mixtures. The theory is a generalization of the optimized cluster theory for single component molecular fluids. Starting from exact cluster expansions for the Helmholtz free energy and pair-correlation functions in a molecular mixture developed by Chandler et al., a series of transformations was performed to yield approximate expressions for these quantities. The resulting theory was demonstrated to be equivalent to a set of diagrammatically proper integral equations. For model isotopic polyethylene blends, we calculated the various partial structure factors in the mixture and used them to predict the compositional dependence of χS. The calculated values of χS were found to be in reasonable agreement with recent neutron-scattering measurements but the theory underestimates the compositional dependence relative to the experiment. Deviations from random mixing that extend well beyond monomeric length scales were predicted in this blend system.